The common difference is equal the difference between the given terms divide by the difference between the term numbers:
[tex]d=\dfrac{a_{28}-a_{17}}{28-17}\to d=\dfrac{-73-(-40)}{11}=\dfrac{-33}{11}=-3[/tex]
Calculate the first term:
[tex]a_1=a_{17}-16d\\\\a_1=-40-16(-3)=-40+48=8[/tex]
The recursive formula is:
[tex] a_n=\left\{\begin{array}{ccc}a_1=8\\a_{n+1}=a_n-3\end{array}\right [/tex]
